Properties of disturbance waves in vertical annular two-phase flow

Disturbance waves play an important role in interfacial transfer of mass, momentum and energy in annular two-phase flow. In spite of their importance, majority of the experimental data available in literature on disturbance wave properties such as velocity, frequency, wavelength and amplitude are limited to near atmospheric conditions (Azzopardi, B.J., 1997. Drops in annular two-phase flow. International Journal of Multiphase Flow, 23, 1-53). In view of this, air-water annular flow experiments have been conducted at three pressure conditions (1.2, 4.0 and 5.8 bar) in a tubular test section having an inside diameter 9.4 mm. At each pressure condition liquid and gas phase flow rates are varied over a large range so that the effects of density ratio, liquid flow rate and gas flow rate on disturbance wave properties can be studied systematically. A liquid film thickness is measured by two flush mounted ring shaped conductance probes located 38.1 mm apart. Disturbance wave velocity, frequency, amplitude and wavelength are estimated from the liquid film thickness measurements by following the statistical analysis methods. Parametric trends in variations of disturbance wave properties are analyzed using the non-dimensional numbers; liquid phase Reynolds number (Re_f), gas phase Reynolds number (Re_g), Weber number (We) and Strouhal number (Sr). Finally, the existing correlations available for the prediction of disturbance wave velocity and frequency are analyzed and a new, improved correlation is proposed for the prediction of disturbance wave frequency. The new correlation satisfactorily predicted the current data and the data available in literature.     

A reinterpretation of measurements in developing annular two-phase flow

Measurements of developing films in adiabatic high pressure steam-water flow in annular geometry have been reanalyzed and compared to a linearized film-flow model. The development rate of the outer film could be determined with good accuracy in four cases. In one case it was also possible to conclude that the inner film develops faster than the outer one. When compared to the linearized model, these observations show that the deposition rate has to be almost independent of the drop concentration at the investigated conditions. Furthermore, any significant deposition by direct impaction of drops can be excluded as it would couple the development of the two films. These conclusions are quite general and do not depend on the use of any particular correlation for the deposition or entrainment rates. Finally, a rough estimate of the deposition rate was possible, confirming that deposition rates are considerably lower at high pressure steam-water flows than in air-water flows.     

Two-group interfacial area transport in vertical air-water flow -II. Model evaluation

In a companion paper, mechanistic models of major fluid particle interaction phenomena involving two bubble groups have been proposed. The prediction of interfacial area concentration evolution using the one-dimensional two-group transport equation and evaluation with experimental results are performed in the paper. These evaluations are based on solid databases for a 2-inch air-water loop with sufficient information on the axial development and the radial distribution of the local parameters. Model evaluation strategies are systematically analyzed. The predictions for the interfacial area concentration evolution demonstrate satisfactory accuracy. The proposed model predicts a smooth transition across the bubbly-to-slug flow regime boundary and demonstrates mechanisms for the generation and development of the cap/slug bubble group. The two-group interfacial area transport equation covers a wide range from bubbly, slug, to churn turbulent flow regimes for adiabatic air-water upward flow in moderate diameter pipes. The generality of the interfacial transport model is also discussed.     

Droplet entrainment correlation in vertical upward co-current annular two-phase flow

Upward annular two-phase flow in a vertical tube is characterized by the presence of liquid film on the tube wall and entrained droplet laden gas phase flowing through the tube core. Entrainment fraction in annular flow is defined as a fraction of the total liquid flow flowing in the form of droplets through the central gas core. Its prediction is important for the estimation of pressure drop and dryout in annular flow. In the following study, measurements of entrainment fraction have been obtained in vertical upward co-current air–water annular flow covering wide ranges of pressure and flow conditions. Comparison of the experimental data with the existing entrainment fraction prediction correlations revealed their inadequacies in simulating the trends observed under high flow and high pressure conditions. Furthermore, several correlations available in the literature are implicit and require iterative calculations.Analysis of the experimental data showed that the non-dimensional numbers, Weber number (We = ρ_gj_g²D/σ(Δρ/ρ_g)^1/4) and liquid phase Reynolds number (Re_f = ρ_fj_fD/μ_f), successfully collapse the data. In view of this, simple, explicit correlation was developed based on these non-dimensional numbers for the prediction of entrainment fraction. The new correlation successfully predicted the trends under the high flow and high pressure conditions observed in the current experimental data and the data available in open literature. However, in order to use the proposed correlation it is necessary to predict the maximum possible entrainment fraction (or limiting entrainment fraction). In the current analysis, an experimental data based correlation was used for this purpose. However, a better model or correlation is necessary for the maximum possible entrainment fraction. A theoretical discussion on the mechanism and modeling of the maximum possible entrainment fraction condition is presented.     

Disturbance wave frequencies, velocities and spacing in vertical annular two-phase flow

A systematic study of disturbance wave properties in annular flow is reported. Frequencies and velocities were deduced from correlational analysis of film thickness records. The data is shown to agree with the more reliable earlier studies, though these were not so extensive. The spacing between waves has also been deduced. The effects of flow rates on this parameter are explained and its relationship to wave height is examined.     

A self-standing two-fluid CFD model for vertical upward two-phase annular flow

In this paper, a new two-fluid CFD (computational fluid dynamics) model is proposed to simulate the vertical upward two-phase annular flow. This model solves the basic mass and momentum equations for the gas core region flow and the liquid film flow, where the basic governing equations are accounted for by the commercial CFD package Fluent6.3.26^®. The liquid droplet flow and the interfacial inter-phase effects are accounted for by the programmable interface of Fluent, UDF (user defined function). Unlike previous models, the present model includes the effect of liquid roll waves directly determined from the CFD code. It is able to provide more detailed and, the most important, self-standing information for both the gas core flow and the film flow as well as the inner tube wall situations.     

Film flow measurements for high-pressure diabatic annular flow in tubes with various axial power distributions

Measurements of film flow rates in diabatic annular flow in tubes with various axial power distributions were carried out in the high-pressure two-phase flow loop at the Royal Institute of Technology (KTH), Sweden. The measurements were performed at conditions typical for boiling water reactors, i.e. 7 MPa pressure and total mass flux in a range from 750 to 1750 kg/m²s. Four different axial power distributions were used and the film mass flow was measured at 7 axial locations for each set of boundary conditions. The results show that the outlet peaked distribution gives less film than the inlet peaked one. This result is consistent with well known trends from measurements of dryout power. The measurements also show that the film flow at the onset of dryout is very small at investigated conditions in agreement with earlier studies. Finally it is shown that the present data is well predicted by two selected phenomenological models of annular flow.     

Experimental investigation of heat transfer for supercritical pressure water flowing in vertical annular channels

An experiment has recently been completed at Xi’an Jiaotong University (XJTU) to obtain wall-temperature measurements at supercritical pressures with upward flow of water inside vertical annuli. Two annular test sections were constructed with annular gaps of 4 and 6 mm, respectively, and an internal heater of 8 mm outer diameter. Experimental-parameter ranges covered pressures of 23-28 MPa, mass fluxes of 350-1000 kg/m²/s, heat fluxes of 200-1000 kW/m², and bulk inlet temperatures up to 400 °C. Depending on the flow conditions and heat fluxes, two distinctive heat transfer regimes, referring to as the normal heat transfer and deteriorated heat transfer, have been observed. At similar flow conditions, the heat transfer coefficients for the 6 mm gap annular channel are larger than those for the 4 mm gap annular channel. A strong effect of spiral spacer on heat transfer has been observed with a drastic reduction in wall temperature at locations downstream of the device in the annuli. Two tube-data-based correlations have been assessed against the experimental heat transfer results. The Jackson correlation agrees with the experimental trends and overpredicts slightly the heat transfer coefficients. The Dittus-Boelter correlation is applicable only for the normal heat transfer region but not for the deteriorated heat transfer region.     

Flooding correlation based on the concept of hyperbolicity breaking in a vertical annular flow

Flooding is classified into exit flooding and entrance flooding depending on the positions at which it is initiated. It is postulated that flooding may result from the instabilities of roll waves and the stationary wave generated at the entrance and the exit respectively. Based on the two-fluid model, the neutral stability condition for wave instabilities is derived by studying hyperbolicity breaking near a singular point in two-phase flow. It turns out to be a type of onset condition of Helmholtz instability; the critical relative velocity depends on the void fraction derivative of the interfacial pressure force as well as on the void fraction and density ratio. In order to obtain information on the interfacial pressure force, a Korteweg-de Vries solitary wave is studied with the assumption that its wavenumber is the same as that of the fastest-growing sine wave. Predictions by the correlations for entrance flooding and exit flooding are in good agreement with experimental data. Also, the present model is able to consider the effect of the test section length on flooding.     

Characteristics and behavior of the interfacial wave on the liquid film in a vertically upward air-water two-phase annular flow

The behavior of individual interfacial waves on liquid film in vertically upward air-water annular flows has been visualized, observed and analyzed by a pigment luminance method(PLM) which was calibrated with a fiber-optic liquid film sensor. By means of this technique, we distinguished three different types of interfacial waves, i.e. the ripple wave, the ring wave and the disturbance wave. Furthermore we measured the characteristics of these three different kinds of waves, and in particular those of the disturbance wave: i.e. its propagation velocity, its frequency in passing and the distance between two adjacent waves, and then obtained the dependency of these characteristics on the air and water volumetric fluxes j_g and j_l. These results agreed well with the results obtained by other investigators, using an electric needle contact method. A probable mechanism of the occurrence of the ring and the disturbance waves was posited.     

Influence of a flow obstacle on the occurrence of burnout in boiling two-phase upward flow within a vertical annular channel

When a flow obstruction such as a cylindrical spacer is set in a boiling two-phase flow within an annular channel, the inner tube of which is used as a heater, the temperature on the surface of the heating tube is severely affected by its existence. In some cases, the cylindrical spacer has a cooling effect, and in the other cases it causes the dryout of the cooling water film on the heating surface resulting in the burnout of the heating tube.In the present paper, we have focused our attention on the influence of a flow obstacle on the occurrence of burnout of the heating tube in boiling two-phase flow.The results are summarized as follows:

(1)When the heat flux approaches the burnout condition, the wall temperature on the heating tube fluctuates with a large amplitude. And once the wall temperature exceeds the Leidenfrost temperature, the burnout occurs without exception.

(2)The trigger of dryout of the water film which causes the burnout is not the nucleate boiling but the evaporation of the base film between disturbance waves.

(3)The burnout never occurs at the downstream side of the spacer. This is because the dryout area downstream of the spacer is rewetted easily by the disturbance waves.

     

On the occurrence of burnout downstream of a flow obstacle in boiling two-phase upward flow within a vertical annular channel

If a flow obstacle, such as a spacer is placed in a boiling two-phase flow within a channel, the temperature on the surface of the heating tube is severely affected by the existence of the spacer. Under certain conditions, a spacer has a cooling effect, and under other conditions, the spacer causes dryout of the cooling water film on the heating surface. The burnout mechanism, which always occurs upstream of a spacer, however, remains unclear.In a previous paper [Fukano, T., Mori, S., Akamatsu, S., Baba, A., 2002. Relation between temperature fluctuation of a heating surface and generation of drypatch caused by a cylindrical spacer in a vertical boiling two-phase upward flow in a narrow annular channel. Nucl. Eng. Des. 217, 81–90], we reported that the disturbance wave has a significant effect on dryout and burnout occurrence and that a spacer greatly affects the behavior of the liquid film downstream of the spacer.In the present study, we examined in detail the influences of a spacer on the heat transfer and film thickness characteristics downstream of the spacer by considering the result in steam–water and air–water systems. The main results are summarized as follows:

(1) The spacer averages the liquid film in the disturbance wave flow. As a result, dryout tends not to occur downstream of the spacer. This means that large temperature increases do not occur there. However, traces of disturbance waves remain, even if the disturbance waves are averaged by the spacer.

(2) There is a high probability that the location at which burnout occurs is upstream of the downstream spacer, irrespective of the spacer spacing.

(3) The newly proposed burnout occurrence model can explain the phenomena that burnout does occur upstream of the downstream spacer, even if the liquid film thickness t_F m is approximately the same before and behind the spacer.

Pressure wave propagation in air-water bubbly and slug flow

Related to nuclear reactor safety problems, such as the loss of coolant accident caused by some small crevasses in nuclear reactor, choked flows after postulated breaks of hot and cold legs of pressurized water reactors and the boiling flow instability in parallel channels, the characteristics of pressure wave propagation were investigated experimentally for the air-water bubbly and slug two-phase flow in a vertical pipe. Pressure wave was generated from the small pressure disturbance by the up-and-down movement of piston in the test section. Air void fraction was up to 0.7 and superficial liquid velocity was up to 1.5 m/s as experimental conditions. The experimental results show that the pressure wave propagation velocity in bubbly flow decreases acutely with the increase of air void fraction from 0 to 0.05. In slug flow, it is constant when the air void fraction is less than 0.5 but increases gradually when the void fraction increases beyond 0.5. The attenuation coefficient of pressure wave increases with the increase of air void fraction in bubbly flow. The dependency of pressure wave propagation velocity on angle frequency ω in air-water flow shows the dispersion characteristic. The propagation velocity and attenuation coefficient increases gradually with the increase of angle frequency. However, the increase vanishes slowly as the angle frequency reaches 250 Hz in bubbly flow. The propagation of pressure wave in bubbly flow is independent of the superficial velocity of fluids in the range of experiment.     

Relation between the occurrence of Burnout and differential pressure fluctuation characteristics caused by the disturbance waves passing by a flow obstacle in a vertical boiling two-phase upward flow in a narrow annular channel

If a flow obstacle such as a spacer is placed in a boiling two-phase flow within a channel, the temperature on the surface of the heating tube is severely affected by the existence of the spacer. Under certain conditions the spacer has a cooling effect, and under other conditions the spacer causes dryout of the cooling water film on the heating surface, resulting in burnout of the tube. The burnout mechanism near the spacer, however, remains unclear.In a previous paper (Fukano, T., Mori, S., Akamatsu, S., Baba, A., 2002. Relation between temperature fluctuation of a heating surface and generation of drypatch caused by a cylindrical spacer in a vertical boiling two-phase upward flow in a narrow annular channel. Nucl. Eng. Des. 217, 81–90), we reported that the disturbance wave has a significant effect on dryout occurrence. Therefore, in the present paper, the relation between dryout, burnout occurrence, and interval between two successive disturbance waves obtained from the differential pressure fluctuation caused by the disturbance waves passing by a spacer, is further discussed in detail.     

Fluctuation characteristics of heating surface temperature near an obstacle in transient boiling two-phase flow in a vertical annular channel

When a flow obstruction such as a spacer is set in a boiling two-phase flow within an annular channel, the inner tube of which is used as a heater, the temperature on the surface of the heater tube is severely affected by the existence of the spacer. In some cases the spacer has a cooling effect, and in other cases it causes the dryout of the cooling water film on the heating surface resulting in the burnout of the tube. In the present paper we will discuss temperature fluctuations in relation to the change in the flow configuration near the cylindrical spacer in transient boiling two-phase flow caused by the stepwise change of the operation parameters such as the heat flux, the mass flow rate, and the inlet quality of the test section. As a result it is concluded that: Even if the flow pattern changes rapidly by a stepwise change of an operation parameter, the transition of flow proceeds safely provided that the change causes the increase of vapor velocity, i.e. the increase of the shear force which is acting on liquid film flow. On the other hand if the change causes the decrease of the vapor velocity, it must be noticed that the transient burnout possibly occurs even when the operating condition after the change is less than the steady burnout condition.     

Flooding and flow reversal of two-phase annular flow

The flooding and flow reversal conditions of two-phase annular flow are mathematically defined in terms of a characteristic function representing a force balance. Sufficiently below the flooding point in counter-current flow, the interface is smooth and the characteristic equation reduces to the Nusselt relationship. Just below the flooding point and above the flow reversal point in cocurrent flow, the interface is “wavy”, so that the interfacial shear effect plays an important role. The theoretical analysis is compared with experimental results by others. It is suggested that the various length effects which have been experimentally observed may be accounted for by the spatial variation of the droplet entrainment.     

Limiting countercurrent flow phenomenon in small break LOCA transients

Countercurrent flow limit phenomena in the loops of a PWR affects small break LOCA transients significantly. This paper reviews the countercurrent flow at three different locations in the loop to identify a limiting phenomenon during a cold leg small break.It is believed that the limiting phenomenon occurs at the inclined pipe which connects the hot leg to the steam generator. Therefore this phenomenon must be simulated properly in any numerical of physical simulations of small break LOCA's. It is pointed out that data from any test loops with scaling have to be analyzed with caution. Distortions in the flow areas of the steam generator tubes and hot leg may result in nontypical transients.     

Effect of steam condensation on countercurrent flow limiting in nearly horizontal two-phase flow

An analytical model that includes the steam condensation effect has been derived and a parametric study has been performed. In addition, a series of experiments were performed and a total of 34 experimental data for the onset of countercurrent flow limiting (CCFL) in nearly horizontal countercurrent two-phase flow have been obtained for various flow rates of water. Comparisons of the present CCFL data with slug formation models show that the agreement between the present as well as the existing model and the data is about the same. However, the deviation between Taitel and Dukler’s model predictions and the data is the largest when j_f<0.04 m s⁻¹. A parametric study of the effect of condensation using the present model shows that, when all local conditions are similar, the model predicted local gas velocities that cause the onset of flooding are slightly lower when condensation occurred. Based on the visual observation and the evaluation of the present work, it has been concluded that the criterion derived for the onset of slug flow can be directly used to predict the onset of inner flooding in nearly horizontal two-phase flow within the experimental ranges of the present work.     

向上倾斜管内气-水两相流流型转变分析

对管径15 mm,管长6 m的有机玻璃管,在两种不同的向上倾斜角度(15°、30°)下,同向通过的气水两相流流型转变进行了分析,列出相应的转变准则关系式。结果显示,弹状流向泡状流转变界限的实验值与计算符合较好,间歇流向环状流的转变界限在低液体流速下符合较好。